{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Use Closed-Form Policy to Play Taxi-v3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import logging\n",
    "import itertools\n",
    "\n",
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "import gym\n",
    "\n",
    "logging.basicConfig(level=logging.DEBUG,\n",
    "        format='%(asctime)s [%(levelname)s] %(message)s',\n",
    "        stream=sys.stdout, datefmt='%H:%M:%S')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "00:00:00 [INFO] id: Taxi-v3\n",
      "00:00:00 [INFO] entry_point: gym.envs.toy_text:TaxiEnv\n",
      "00:00:00 [INFO] reward_threshold: 8\n",
      "00:00:00 [INFO] nondeterministic: False\n",
      "00:00:00 [INFO] max_episode_steps: 200\n",
      "00:00:00 [INFO] order_enforce: True\n",
      "00:00:00 [INFO] _kwargs: {}\n",
      "00:00:00 [INFO] _env_name: Taxi\n",
      "00:00:00 [INFO] desc: [[b'+' b'-' b'-' b'-' b'-' b'-' b'-' b'-' b'-' b'-' b'+']\n",
      " [b'|' b'R' b':' b' ' b'|' b' ' b':' b' ' b':' b'G' b'|']\n",
      " [b'|' b' ' b':' b' ' b'|' b' ' b':' b' ' b':' b' ' b'|']\n",
      " [b'|' b' ' b':' b' ' b':' b' ' b':' b' ' b':' b' ' b'|']\n",
      " [b'|' b' ' b'|' b' ' b':' b' ' b'|' b' ' b':' b' ' b'|']\n",
      " [b'|' b'Y' b'|' b' ' b':' b' ' b'|' b'B' b':' b' ' b'|']\n",
      " [b'+' b'-' b'-' b'-' b'-' b'-' b'-' b'-' b'-' b'-' b'+']]\n",
      "00:00:00 [INFO] locs: [(0, 0), (0, 4), (4, 0), (4, 3)]\n",
      "00:00:00 [INFO] P: {0: {0: [(1.0, 100, -1, False)], 1: [(1.0, 0, -1, False)], 2: [(1.0, 20, -1, False)], 3: [(1.0, 0, -1, False)], 4: [(1.0, 16, -1, False)], 5: [(1.0, 0, -10, False)]}, 1: {0: [(1.0, 101, -1, False)], 1: [(1.0, 1, -1, False)], 2: [(1.0, 21, -1, False)], 3: [(1.0, 1, -1, False)], 4: [(1.0, 17, -1, False)], 5: [(1.0, 1, -10, False)]}, 2: {0: [(1.0, 102, -1, False)], 1: [(1.0, 2, -1, False)], 2: [(1.0, 22, -1, False)], 3: [(1.0, 2, -1, False)], 4: [(1.0, 18, -1, False)], 5: [(1.0, 2, -10, False)]}, 3: {0: [(1.0, 103, -1, False)], 1: [(1.0, 3, -1, False)], 2: [(1.0, 23, -1, False)], 3: [(1.0, 3, -1, False)], 4: [(1.0, 19, -1, False)], 5: [(1.0, 3, -10, False)]}, 4: {0: [(1.0, 104, -1, False)], 1: [(1.0, 4, -1, False)], 2: [(1.0, 24, -1, False)], 3: [(1.0, 4, -1, False)], 4: [(1.0, 4, -10, False)], 5: [(1.0, 4, -10, False)]}, 5: {0: [(1.0, 105, -1, False)], 1: [(1.0, 5, -1, False)], 2: [(1.0, 25, -1, False)], 3: [(1.0, 5, -1, False)], 4: [(1.0, 5, -10, False)], 5: 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-1, False)]}, 478: {0: [(1.0, 478, -1, False)], 1: [(1.0, 378, -1, False)], 2: [(1.0, 498, -1, False)], 3: [(1.0, 478, -1, False)], 4: [(1.0, 478, -10, False)], 5: [(1.0, 474, -1, False)]}, 479: {0: [(1.0, 479, -1, False)], 1: [(1.0, 379, -1, False)], 2: [(1.0, 499, -1, False)], 3: [(1.0, 479, -1, False)], 4: [(1.0, 479, -10, False)], 5: [(1.0, 475, 20, True)]}, 480: {0: [(1.0, 480, -1, False)], 1: [(1.0, 380, -1, False)], 2: [(1.0, 480, -1, False)], 3: [(1.0, 460, -1, False)], 4: [(1.0, 480, -10, False)], 5: [(1.0, 480, -10, False)]}, 481: {0: [(1.0, 481, -1, False)], 1: [(1.0, 381, -1, False)], 2: [(1.0, 481, -1, False)], 3: [(1.0, 461, -1, False)], 4: [(1.0, 481, -10, False)], 5: [(1.0, 481, -10, False)]}, 482: {0: [(1.0, 482, -1, False)], 1: [(1.0, 382, -1, False)], 2: [(1.0, 482, -1, False)], 3: [(1.0, 462, -1, False)], 4: [(1.0, 482, -10, False)], 5: [(1.0, 482, -10, False)]}, 483: {0: [(1.0, 483, -1, False)], 1: [(1.0, 383, -1, False)], 2: [(1.0, 483, -1, False)], 3: [(1.0, 463, -1, False)], 4: [(1.0, 483, -10, False)], 5: [(1.0, 483, -10, False)]}, 484: {0: [(1.0, 484, -1, False)], 1: [(1.0, 384, -1, False)], 2: [(1.0, 484, -1, False)], 3: [(1.0, 464, -1, False)], 4: [(1.0, 484, -10, False)], 5: [(1.0, 484, -10, False)]}, 485: {0: [(1.0, 485, -1, False)], 1: [(1.0, 385, -1, False)], 2: [(1.0, 485, -1, False)], 3: [(1.0, 465, -1, False)], 4: [(1.0, 485, -10, False)], 5: [(1.0, 485, -10, False)]}, 486: {0: [(1.0, 486, -1, False)], 1: [(1.0, 386, -1, False)], 2: [(1.0, 486, -1, False)], 3: [(1.0, 466, -1, False)], 4: [(1.0, 486, -10, False)], 5: [(1.0, 486, -10, False)]}, 487: {0: [(1.0, 487, -1, False)], 1: [(1.0, 387, -1, False)], 2: [(1.0, 487, -1, False)], 3: [(1.0, 467, -1, False)], 4: [(1.0, 487, -10, False)], 5: [(1.0, 487, -10, False)]}, 488: {0: [(1.0, 488, -1, False)], 1: [(1.0, 388, -1, False)], 2: [(1.0, 488, -1, False)], 3: [(1.0, 468, -1, False)], 4: [(1.0, 488, -10, False)], 5: [(1.0, 488, -10, False)]}, 489: {0: [(1.0, 489, -1, False)], 1: [(1.0, 389, -1, False)], 2: [(1.0, 489, -1, False)], 3: [(1.0, 469, -1, False)], 4: [(1.0, 489, -10, False)], 5: [(1.0, 489, -10, False)]}, 490: {0: [(1.0, 490, -1, False)], 1: [(1.0, 390, -1, False)], 2: [(1.0, 490, -1, False)], 3: [(1.0, 470, -1, False)], 4: [(1.0, 490, -10, False)], 5: [(1.0, 490, -10, False)]}, 491: {0: [(1.0, 491, -1, False)], 1: [(1.0, 391, -1, False)], 2: [(1.0, 491, -1, False)], 3: [(1.0, 471, -1, False)], 4: [(1.0, 491, -10, False)], 5: [(1.0, 491, -10, False)]}, 492: {0: [(1.0, 492, -1, False)], 1: [(1.0, 392, -1, False)], 2: [(1.0, 492, -1, False)], 3: [(1.0, 472, -1, False)], 4: [(1.0, 492, -10, False)], 5: [(1.0, 492, -10, False)]}, 493: {0: [(1.0, 493, -1, False)], 1: [(1.0, 393, -1, False)], 2: [(1.0, 493, -1, False)], 3: [(1.0, 473, -1, False)], 4: [(1.0, 493, -10, False)], 5: [(1.0, 493, -10, False)]}, 494: {0: [(1.0, 494, -1, False)], 1: [(1.0, 394, -1, False)], 2: [(1.0, 494, -1, False)], 3: [(1.0, 474, -1, False)], 4: [(1.0, 494, -10, False)], 5: [(1.0, 494, -10, False)]}, 495: {0: [(1.0, 495, -1, False)], 1: [(1.0, 395, -1, False)], 2: [(1.0, 495, -1, False)], 3: [(1.0, 475, -1, False)], 4: [(1.0, 495, -10, False)], 5: [(1.0, 495, -10, False)]}, 496: {0: [(1.0, 496, -1, False)], 1: [(1.0, 396, -1, False)], 2: [(1.0, 496, -1, False)], 3: [(1.0, 476, -1, False)], 4: [(1.0, 496, -10, False)], 5: [(1.0, 496, -10, False)]}, 497: {0: [(1.0, 497, -1, False)], 1: [(1.0, 397, -1, False)], 2: [(1.0, 497, -1, False)], 3: [(1.0, 477, -1, False)], 4: [(1.0, 497, -10, False)], 5: [(1.0, 497, -10, False)]}, 498: {0: [(1.0, 498, -1, False)], 1: [(1.0, 398, -1, False)], 2: [(1.0, 498, -1, False)], 3: [(1.0, 478, -1, False)], 4: [(1.0, 498, -10, False)], 5: [(1.0, 498, -10, False)]}, 499: {0: [(1.0, 499, -1, False)], 1: [(1.0, 399, -1, False)], 2: [(1.0, 499, -1, False)], 3: [(1.0, 479, -1, False)], 4: [(1.0, 499, -10, False)], 5: [(1.0, 499, -10, False)]}}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      " 0.         0.        ]\n",
      "00:00:00 [INFO] lastaction: None\n",
      "00:00:00 [INFO] nS: 500\n",
      "00:00:00 [INFO] nA: 6\n",
      "00:00:00 [INFO] action_space: Discrete(6)\n",
      "00:00:00 [INFO] observation_space: Discrete(500)\n",
      "00:00:00 [INFO] np_random: RandomState(MT19937)\n",
      "00:00:00 [INFO] s: 344\n",
      "00:00:00 [INFO] spec: EnvSpec(Taxi-v3)\n"
     ]
    }
   ],
   "source": [
    "env = gym.make('Taxi-v3')\n",
    "env.seed(0)\n",
    "for key in vars(env.spec):\n",
    "    logging.info('%s: %s', key, vars(env.spec)[key])\n",
    "for key in vars(env.unwrapped):\n",
    "    logging.info('%s: %s', key, vars(env.unwrapped)[key])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ClosedFormAgent:\n",
    "    def __init__(self, env):\n",
    "        state_n, action_n = env.observation_space.n, env.action_space.n\n",
    "        v = np.zeros((env.spec.max_episode_steps+1, state_n))\n",
    "        q = np.zeros((env.spec.max_episode_steps+1, state_n, action_n))\n",
    "        pi = np.zeros((env.spec.max_episode_steps+1, state_n))\n",
    "        for t in range(env.spec.max_episode_steps-1, -1, -1):\n",
    "            for s in range(state_n):\n",
    "                for a in range(action_n):\n",
    "                    for p, next_s, r, d in env.P[s][a]:\n",
    "                        q[t, s, a] += p * (r + (1. - float(d)) * v[t+1, next_s])\n",
    "                v[t, s] = q[t, s].max()\n",
    "                pi[t, s] = q[t, s].argmax()\n",
    "        self.pi = pi\n",
    "\n",
    "    def reset(self, mode=None):\n",
    "        self.t = 0\n",
    "\n",
    "    def step(self, observation, _reward, _done):\n",
    "        action = self.pi[self.t, observation]\n",
    "        self.t += 1\n",
    "        return action\n",
    "\n",
    "    def close(self):\n",
    "        pass\n",
    "\n",
    "\n",
    "agent = ClosedFormAgent(env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "00:00:01 [INFO] ==== test ====\n",
      "00:00:01 [DEBUG] test episode 0: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 1: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 2: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 3: reward = 11.00, steps = 10\n",
      "00:00:01 [DEBUG] test episode 4: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 5: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 6: reward = 11.00, steps = 10\n",
      "00:00:01 [DEBUG] test episode 7: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 8: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 9: reward = 13.00, steps = 8\n",
      "00:00:01 [DEBUG] test episode 10: reward = 11.00, steps = 10\n",
      "00:00:01 [DEBUG] test episode 11: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 12: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 13: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 14: reward = 13.00, steps = 8\n",
      "00:00:01 [DEBUG] test episode 15: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 16: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 17: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 18: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 19: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 20: reward = 11.00, steps = 10\n",
      "00:00:01 [DEBUG] test episode 21: reward = 12.00, steps = 9\n",
      "00:00:01 [DEBUG] test episode 22: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 23: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 24: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 25: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 26: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 27: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 28: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 29: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 30: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 31: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 32: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 33: reward = 12.00, steps = 9\n",
      "00:00:01 [DEBUG] test episode 34: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 35: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 36: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 37: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 38: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 39: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 40: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 41: reward = 11.00, steps = 10\n",
      "00:00:01 [DEBUG] test episode 42: reward = 13.00, steps = 8\n",
      "00:00:01 [DEBUG] test episode 43: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 44: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 45: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 46: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 47: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 48: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 49: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 50: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 51: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 52: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 53: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 54: reward = 12.00, steps = 9\n",
      "00:00:01 [DEBUG] test episode 55: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 56: reward = 11.00, steps = 10\n",
      "00:00:01 [DEBUG] test episode 57: reward = 3.00, steps = 18\n",
      "00:00:01 [DEBUG] test episode 58: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 59: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 60: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 61: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 62: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 63: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 64: reward = 13.00, steps = 8\n",
      "00:00:01 [DEBUG] test episode 65: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 66: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 67: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 68: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 69: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 70: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 71: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 72: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 73: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 74: reward = 11.00, steps = 10\n",
      "00:00:01 [DEBUG] test episode 75: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 76: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 77: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 78: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 79: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 80: reward = 12.00, steps = 9\n",
      "00:00:01 [DEBUG] test episode 81: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 82: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 83: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 84: reward = 12.00, steps = 9\n",
      "00:00:01 [DEBUG] test episode 85: reward = 14.00, steps = 7\n",
      "00:00:01 [DEBUG] test episode 86: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 87: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 88: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 89: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 90: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 91: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 92: reward = 9.00, steps = 12\n",
      "00:00:01 [DEBUG] test episode 93: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 94: reward = 6.00, steps = 15\n",
      "00:00:01 [DEBUG] test episode 95: reward = 7.00, steps = 14\n",
      "00:00:01 [DEBUG] test episode 96: reward = 10.00, steps = 11\n",
      "00:00:01 [DEBUG] test episode 97: reward = 8.00, steps = 13\n",
      "00:00:01 [DEBUG] test episode 98: reward = 4.00, steps = 17\n",
      "00:00:01 [DEBUG] test episode 99: reward = 8.00, steps = 13\n",
      "00:00:01 [INFO] average episode reward = 8.04 ± 2.53\n"
     ]
    }
   ],
   "source": [
    "def play_episode(env, agent, max_episode_steps=None, mode=None, render=False):\n",
    "    observation, reward, done = env.reset(), 0., False\n",
    "    agent.reset(mode=mode)\n",
    "    episode_reward, elapsed_steps = 0., 0\n",
    "    while True:\n",
    "        action = agent.step(observation, reward, done)\n",
    "        if render:\n",
    "            env.render()\n",
    "        if done:\n",
    "            break\n",
    "        observation, reward, done, _ = env.step(action)\n",
    "        episode_reward += reward\n",
    "        elapsed_steps += 1\n",
    "        if max_episode_steps and elapsed_steps >= max_episode_steps:\n",
    "            break\n",
    "    agent.close()\n",
    "    return episode_reward, elapsed_steps\n",
    "\n",
    "\n",
    "logging.info('==== test ====')\n",
    "episode_rewards = []\n",
    "for episode in range(100):\n",
    "    episode_reward, elapsed_steps = play_episode(env, agent)\n",
    "    episode_rewards.append(episode_reward)\n",
    "    logging.debug('test episode %d: reward = %.2f, steps = %d',\n",
    "            episode, episode_reward, elapsed_steps)\n",
    "logging.info('average episode reward = %.2f ± %.2f',\n",
    "        np.mean(episode_rewards), np.std(episode_rewards))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "env.close()"
   ]
  }
 ],
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